University of Bath · the forward problem, the ﬁnite element method (FEM) is employed to evaluate the ﬁeld distribution. This is then used to derive a sensitivity matrix that

Citation for published version:Ma, L & Soleimani, M 2017, 'Magnetic induction tomography methods and applications: a review', MeasurementScience and Technology, vol. 28, no. 7, 072001. https://doi.org/10.1088/1361-6501/aa7107

DOI:10.1088/1361-6501/aa7107

Publication date:2017

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Methods and Applications of Magnetic Induction

Tomography: A review

Lu Ma and Manuchehr Soleimani

Engineering Tomography Laboratory (ETL), Department of Electronic andElectrical Engineering, University of Bath, Bath, BA2 7AY, UK

E-mail: [email protected] and [email protected]

Abstract. Magnetic induction tomography (MIT) is a tomographic techniquecapable of imaging the passive electromagnetic properties of an object. Ithas the advantages of being contact-less and non-invasive, as the processinvolves interrogating the electromagnetic field of the imaging subject. Assuch, the potential applications of MIT are broad, with various domainsof operation including biomedicine, industrial process tomography and non-destructive evaluation. Consequently, there is a rich – yet underexplored –research landscape for the practical applications of MIT. The aim of this reviewis to provide a non-exhaustive overview of this landscape. The fundamentalprinciples of MIT are discussed, alongside the instrumentation and techniquesnecessary to obtain and interpret MIT measurements.

Keywords: magnetic induction tomography, industrial process tomography, non-destructive evaluation, biomedical imaging, eddy current forward problem, MITinverse problem

Methods and Applications of Magnetic Induction Tomography: A review 2

1. Introduction

Magnetic induction tomography (MIT) utilises inductive sensing coils to map theelectromagnetic properties of an object. As this is a non-intrusive, non-nuclear andcontactless technique, it has many potential applications spanning a diverse rangeof problems and industrial challenges, from biomedical imaging through to non-destructive testing. The development of MIT, in terms of both instrumentationand software, has been given by [1, 2]. A broader overview, covering the theories,systems and potential applications of MIT, was published in [3], as have reviews ofspecific MIT research advances, such as transmitters and sensors [4]. The aim of thisreview is to provide an overview of the current research landscape for MIT, discussingthe advances, limitations and direction for the future improvement of MIT for threeapplications: biomedical imaging, industrial process tomography and non-destructiveevaluation. To demonstrate how the fundamental theories of MIT can be appliedacross these differing domains, a generic forward formulation and inverse solver willfirst be discussed in a step-by-step fashion.

The fundamental principles of MIT can be explained using basic mutualinductance and eddy current theories (Figure 1) [5, 6]. In brief, by passing analternating current through one or more excitation coils, a primary magnetic fieldis generated that induces an electric field detectable by one or more measuring coils.From this electric field the induced voltage can then be measured. If a conductiveobject is placed within this field, an eddy current arises, which can also generate amagnetic field – known as the secondary field. Consequently, the electric field on themeasuring coil is induced, in part, by both the primary and secondary fields. Theinduced voltages on the measuring coil will therefore differ depending on whether aconductive object is present within the field. If no such object is present, the inducedvoltage arises entirely due to the primary field, whereas if an object is present, theinduced voltage arises due to both primary and secondary fields. By analysing thedifference in the induced voltages, various properties of the conductive object can bereconstructed.

Figure 1. Fundamental principles of MIT.


2. Methods

In MIT, a time-varying current is used in the excitation coil(s) and sensing coils areused to measure the resulting induced voltages. For model-based image reconstruction,the MIT measuring process needs to be simulated, which is called the MIT forwardproblem. The forward problem is a classic eddy current problem and has beenextensively studied in computational electromagnetics using a combination of themagnetic vector potential A, magnetic scalar potential and electric scalar potential�, all of which are fundamentally derived from Maxwell’s equations [7, 8, 9, 10]. Theeddy current formulation has to comply to both the uniqueness of the fields andthe boundary conditions. Difficulties arise when relative boundary conditions areapplied, leading to solutions of variable accuracy. For imaging subjects with a simpleconfiguration and a high degree of symmetry, an analytical solution might be appliedfor linear image reconstruction [11]. However, if the desired image needs to be morerealistic, the forward problem cannot be solved this way. For a general solution ofthe forward problem, the finite element method (FEM) is employed to evaluate thefield distribution. This is then used to derive a sensitivity matrix that describes theperturbation in the receiving voltage caused by changes in the electrical propertiesof the imaging subject [12, 13, 14, 15, 16]. In this article, a (A, A) formulation withedge-finite elements – widely used in MIT forward models – is presented [17].

2.1. Electromagnetic field modelling

In general, the forward problem is solved using full Maxwell’s equations. Forsimplicity, the MIT forward problem can be solved under the condition of a quasi-static electromagnetic field with a few assumptions. First, the displacement currentis neglected (when � >> !" ); second, the material is considered to have an isotropiccharacter (the effect of material with unisotropical character has been studied in [18]);third, the eddy current effect in the current source is also neglected (when Js >> Je).Note that there are two regions in the quasi-static electromagnetic field, the non-conducting region and the eddy current region (Figure 2).

Figure 2. Regions of operation for an MIT system, including a non-conducingregion and an eddy current region with an inductive coil located in the proximity.


Using the time-harmonic notation of Maxwell’s equations, in the eddy current region⌦e:

r⇥H = Je (1)

r⇥ E = �dB

dt(2)

r ·B = 0 (3)

In the non-conducting region ⌦n:r⇥H = Js (4)

r ·B = 0 (5)

In each region, the B and H fields satisfy that the normal component of the B field iszero and the tangential component of the H field is zero. On the boundary betweenthe two regions �ne:

Be · ne +Bn · nn = 0 (6)

He ⇥ ne +Hn ⇥ nn = 0 (7)

where Je is the eddy current density in ⌦e, Js is the current density due to theexcitation in the non-conducting region ⌦n, n is the normal vector on the boundary,and Be, He, ne, Bn, Hn, nn refer to the the magnetic flux, magnetic field and normalvectors in regions of ⌦e and ⌦n respectively. The uniqueness of B and E are thereforeensured.

2.2. Forward model formulation

In the region of ⌦n + ⌦e the magnetic field density can be expressed by:r⇥H = Js + �E (8)

where Js is the excitation current source in the coil, which can be prescribed bythe magnetic vector potential according to the Biot-Savart Law. E is the inducedelectric field in the region of ⌦n + ⌦e, and � is the conductivity distribution is theeddy current region ⌦e. Note that equation 8 can be extended to include the wavepropagation effect, i.e., � >> !" no longer holds.Ignoring the displacement current, E can be written in the following form:

E = �@A@t

(9)

where the magnetic potential, A, is the sum of two parts: As, the magnetic vectorpotential as result of current source Js (shown in equation 14), and Ae the reducedmagnetic vector potential in the eddy current region ⌦e, and ! is the angular frequency.

A = As +Ae (10)In the region of ⌦n,

r⇥Hs = Js (11)


where Hs is the magnetic field generated by an excitation coil in region ⌦n, which canbe directly computed from in any point P in free space from Js:

Hs =

ˆ⌦n

Js(Q)⇥ rQP

4⇡ | rQP |3 d⌦Q (12)

where rQP is the vector pointing from the source point Q to the field point P .

r⇥As = µ0Hs (13)

Therefore from equations 11,12 and 13, As is readily shown as:

As =

ˆ⌦n

µ0Js(Q)

4⇡ | rQP |2 d⌦Q (14)

Knowing the permeability µ in the region of ⌦e,

H =1

µB (15)

Combining equations 8, 9, 10, 14, and 15:

r⇥ 1

µr⇥ (As +Ae) = r⇥ 1

µ0r⇥As � �

@(As +Ae)

@t(16)

Rearranging equation 16:

1

µr⇥r⇥Ae + �

@Ae

@t=

1

µ0r⇥r⇥As � �

@As

@t� 1

µr⇥r⇥As (17)

In MIT, the inductive coils are considered magneto-static not antennas; as suchthe wave propagation effect can be ignored. By approximating the system asa combination of linear equations in small elements with appropriate boundaryconditions using edge FEM on a tetrahedral mesh, a vector field is represented usinga basis vector function Nij associated with the edge between nodes i and j :

Nij = LirLj � LjrLi (18)

where Li is a nodal shape function. Applying the edge element basis function toGalerkin’s approximation [19, 20, 21, 22], one can obtain:

ˆ⌦e

(1

µr⇥N ·r⇥Ae)dv +

ˆ⌦e

j!�N ·Aedv =

ˆ⌦c

(1

µ0r⇥N ·r⇥As)dv �

ˆ⌦c

(N · j!�As)dv�

�ˆ⌦c

r⇥ (N · 1µµ0r⇥As)dv (19)

where N is any linear combination of edge basis functions, ⌦e is the eddy currentregion, and ⌦c is the coil region. The right hand side in equation 19 can be solvedby equations 12 and 14. The only unknown variable is the reduced vector potentialAe. By applying edge FEM, the second order partial differential equations can becomputed by a combination of system linear equations, which can then be solved.


The Ae can be obtained using the biconjugate gradients stabilized method to solvethe system linear equation [23]:

KAe +MAe = Jrhs (20)

where K and M are the stiffness and math matrices solved by edge FEM, and Jrhsis the right hand side current density.

By solving the reduced magnetic vector potential Ae, one is able to evaluate theinduced voltages in the measuring coils. The induced voltages can be calculated byusing a volume integration form [24]:

VR = �j!

ˆ⌦c

A · J0dv (21)

where J0 is a unit current density following the strands of the receiver coil. Critical toforward modelling is its validation against measured data. Figure 3 shows an exampleof a forward model validation using an eight-coil MIT system with 28 independentmeasurements (the detailed system design and application was described elsewhere[25]). The differences between the simulation and experimental data are noticeable.The possible error sources may include the imperfection of the coil geometricalproperties, electronic errors, numerical errors such as the effect of the mesh density,and the level of convergence for solving the system linear equation (equation 20).Improvements need to be made in both the modelling software and the sensor design,should a fully non-linear and absolute value MIT imaging be materialised in the future.

Figure 3. Comparison of simulated voltages and measured voltages for the samegiven imaging subject.

2.3. Sensitivity formulation

This formulation was derived based on the relationships between the parametersof a test object and its electromagnetic properties, and the extension of Tellegen’stheorem to general electromagnetic problems. In this method, a small change in


material property is related to a small change in a physically measured quantity of theelectromagnetic fields. In other words a physically measured parameter F is expressedas an integral of the electric E and magnetic H fields over some bounded volume.

F =

ˆvf(E,H)dv (22)

Since the fields are the functions of the system parameters, the variations in F can beapproximated with change in system parameters [26].

4F =

ˆv(S�4� + Sµ4µ+ S"4"+ SJs4Js)dv (23)

where F is a function of the electric and magnetic fields, Js is the source current,S represents the sensitivity of the function F to a change in material parameter,and �, µ and " are the material electrical conductivity, permeability and permittivityrespectively.

The sensitivity distribution is caused by a combination of complex electric fieldand magnetic field, which are dependent on the configuration of the coils, geometricaland electrical properties of the background, inclusion, as well as the excitationfrequency. A detailed derivation of the sensitivity terms for different regimes ofmeasurement (amplitude and phase of the induced voltages) are presented in [27].Taking the material conductivity as the subject of interest, the sensitivity formulationcan be written as equation 24.

�Vmn

��k= � !2

ImIn

ˆ⌦k

{Am} · {An}dv (24)

where Vmn is the induced voltage pairs of coils of m,n with respect to an element,�k is the conductivity at element k, ⌦k is the volume of element number k. Im andIn are excitation currents for the coil m and coil n, and Am and An are respectivelysolutions of the forward solver in the eddy currents region (equation 20).

2.4. Image reconstruction algorithm

The inversion of MIT data is an ill-posed inverse problem. As the inverse probleminvolves inverting the sensitivity matrix, this will make the solution unreliableand sensitive to modelling error and measurement noise. Consequently, a smallmeasurement or modelling error could result in a very large change in the reconstructedconductivity profile. Implementing regularisation techniques that involve introducingadditional penalty terms and a smoothing parameter usually mitigates this problem.The inverse problem can usually be formulated in terms of optimising an objectfunction with physical measurements and the goal is to solve the distributionof conductivity (or the other passive electromagnetic properties, formulation hereshows electrical conductivity but applies the same ways for other properties) whilethe measurement signals are given. Solving the inverse problem includes startingwith a trial configuration of the system parameters and subsequently modifyingthis configuration using iterative or non-iterative optimisation algorithms, such aslinear back projection [28], Newton one step error reconstruction [29], Tikhonovregularisation (equation 25) [30], Landweber iteration method [31], or the Laplacianregularisation method [32].

The Tikhonov method has been commonly used for time difference MIT imagereconstruction to overcome the ill-posedness of the inverse problem. In general,


the algorithm in this problem is formulated as a discrete problem that seeks tominimise the discrepancy between the model and the measured data with respectto the conductivity values in a least squares sense, such that the objective function ofthe problem is expressed in the generalised Tikhonov form:

�⇤ = argmin�

�G(�) = kd(�)�2 + ��L(� � �ref )�2

(25)

where �⇤2Rn is the discrete solution of the conductivity vector corresponding to nunknown conductivity values �⇤ = (�1,�2,�3. . . .�n)T and d(�) = (F (�) �M)2Rm sthe residual between the forward operator F (�) and the measurement data M , �refis the user-defined reference conductivity value, and � and L are the regularisationparameter and regularisation operator matrix respectively. The solution to theproblem is found by generating a succession of conductivity vectors {�1,�2,�3. . . ,�⇤}that eventually minimise the objective function G(�). Following 25, the Tikhonovmethod in its iterative form can be expressed as:

4� = (JTk Jk + �LTL)�1JT

k (d(�)) + �LTL(�k � �ref ) (26)

The conductivity profile of the problem domain can then be updated iteratively:

�k+1 = �k +4� (27)

where k is the number of the iteration and �k and Jk are respectively the conductivityand the Jacobian computed on the kth iteration.

3. MIT measurements

3.1. Instrumentation

Regardless of its intended application, a generic MIT system consists of an array ofinductive coils, a data acquisition unit (which obtains measurements from these coils),and a host PC for data analysis and image reconstruction. One should note that thereis no universal design approach for a MIT system, and that the hardware of a MITsystem should be designed to its proposed application. A general consensus – forbiomedical applications – is that a suitable MIT system should be able to resolve 1%of the magnetic field perturbation caused by biological tissues [3]. For this application,as the perturbation caused by biological tissues (which have a conductivity range of0.001S/m to 2S/m) is both very low and proportionate to the driving frequency,then to improve the signal level, frequencies of 1-30MHz have been used to drive theexcitation coils. By contrast, for applications of MIT involving metallic structures(such as non-destructive evaluation), the driving frequency of the excitation coils areusually in the range of 5-500kHz.

However, with higher frequency ranges, amplifiers on the receiver coils will in mostcases experience degraded performance due to ambient and electronic temperaturedrift. Consequently, small drifts in the temperature can result in a large drift inthe phase measurement, with the phase noise and drift increasing over time as thefrequency increases [33]. Amplifiers meeting the requirements of high stability andprecision are usually bespoke and often used in military applications, resulting in amuch higher cost. Careful selection of the amplifier and subsequent design of the phasedetection method are therefore required. Many groups have attempted to increase thesignal detectability, such as by adopting a novel zero flow gradiometer design in theMIT receiving circuit to improve spatial sensitivity and reduce the voltage drift andinterference from far RF sources [34], and by optimising the receiving coils [35].


Figure 4 shows the Bath biomedical MIT system, comprising an excitation unit,an array of 16 air-cored coils shielded by an aluminium ring, a data acquisition andswitching unit, and a host PC for data analysis and image reconstruction.

Figure 4. The complete 16 channel MIT system setup for saline bottle detection,adapted from [36] and reproduced courtesy of The Electromagnetics Academy.

3.2. Measurement techniques

The most commonly used MIT phase detection method is in-phase and quadrature(I/Q) demodulation, the implementation of which is often centred on NationalInstruments (NI) equipment [37]. The I/Q phase demodulation method uses a lock-inamplifier for signal referencing. However, this could compromise the system speed as ittakes time to acquire the clock and pass the clock to other channels. Moreover, there isa transient period associated with its use – it takes time for the electronic componentsto settle. Another drawback of this approach is that data transfer between the NI cardand a PC is not particularly fast. This is particularly notable if the switch-acquire-transfer process is completed sequentially, and could limit MIT performance if rapidinspection or real-time imaging is required. Nevertheless, one distinct advantage isthat any signal jitter when switching between the receivers could be avoided as all theclocks are synchronised due to the implementation of a phase lock-in method.

A direct phase measurement using heterodyne down-conversion on a transceiverwas introduced in [38] and implemented in [39]. This method relies on the fact thatthe widths of the output signals should remain constant if the phase offset betweenthe received and reference signal pulses remain unchanged. Changes in the width of apulsed signal reflect phase changes due to the perturbation of the imaging subject inthe electromagnetic field, and can be measured directly using an oscilloscope with acounter. More in-depth evaluation of the phase noise caused by the down-conversionof these direct measurements was studied in [40]. One potential problem associatedwith this method is the phase skew induced by a low signal amplitude.

Another direct phase measurement is the use of the Fast Fourier Transformalgorithm to measure the phase [41]. This method has the advantage of being fast andparticularly useful for multi-frequency signals. It was shown in [42] that for frequenciesranging from 0.5-14MHz, a phase noise lower that 1millidegree is possible. In addition,it was found that over a 12 hour period of phase measurement, the reported phase


drift was lower than 20 millidegrees. Nevertheless, problems can arise with FTT inthe form of spectral leakage, which can occur if the received signal does not contain anexact number of cycles. This is usually the case for a real-time signal. Good practiceto avoid spectral leakage is to ensure the sample length is in the same range as theresolution of the signal synthesizer.

3.3. Multi-frequency operation

The detectability and imaging capability of MIT could be improved using multi-frequency excitations. This is based on the fundamental principle that conductivityis frequency-dependent. High frequency measurements give information regardingthe properties adjacent to the surface of the imaging subject, whereas low frequencymeasurements probe deeper inside it. The major challenges of implementing multi-frequency MIT are in conditioning electronics and software control. In [43], thehardware electronics and software control were studied to facilitate the implementationof three sinusoidal signals with target frequencies below 1kHz for simultaneousexcitation. This multi-frequency system was proposed for the visualisation of steelflows. As for non-magnetic, electrically conductive metals – i.e., when µr = 1 – asingle frequency might meet the skin depth requirement. However, for other materialssuch as steel, where both conductivity and permeability play important roles, usinga single selected frequency would not be sufficient to accurately reconstruct an imagedifferentiating different steel flow profiles. Hardware development of multifrequencysystems have also been studied for imaging biological tissues, where in [44] the systememployed ten excitation frequencies between 40 and 370kHz and the multi-frequencymeasurements were made using planar gradiometers; while in [45] the multi-frequencyMIT system employed a higher frequency range from 50kHz to 1MHz, the detaileddata collection and calibration on this system were also presented. Therefore it isdesirable to design an excitation channel to provide a range of excitation frequenciessuitable for the imaging target as this could increase the information available to anMIT system, making reconstructed images more robust to anomalies.

Enhancing the MIT software to be able to collect multi-frequency data, alongsidereconstructing spectral and frequency differences, is particularly useful for imagingconductive materials with anisotropic characteristics [18]. Of additional interest isfrequency difference imaging, which could be useful if the test subjects show differentresponses to frequency variation. The reconstruction of pathophysiological informationusing multi-frequency data and frequency dependence sensitivity matrix was studiedin [46], which showed that low resolution similar to those obtained from electricalimpedance tomography is possible.

4. Applications

4.1. Biomedical imaging

Developing an accurate biomedical imaging device for low-cost real time monitoringwould offer considerable diagnostic advantages, particularly when early detectionstrongly influences prognosis – for instance, in the case of brain haemorrhage orcerebral stroke. The most commonly used imaging techniques, X-ray computedtomography and magnetic resonance imaging (MRI), are comparatively expensive.In addition, the diagnostic process may involve hazardous radiation and therefore


cannot be applied to all patients. As such, MIT has attracted interest as an alternativetechnique. However, as biological tissues usually have conductivity lower than 2S/m,then in order to account for any field perturbation, a phase change of 1 millidegreeneeds to be resolved [3]. This is challenging from the perspective of system design.

The first application of MIT to biomedical imaging demonstrated that 0.1 and0.01 mole/l NaCl concentrations (equivalent conductivity of 1S/m and 0.1S/m) indeionized water (which approximate fat-free and fat-rich tissue conductivities) canbe distinguished [47]. In addition to this experimental work, simulations havebeen made of a range of biological tissues, including the spine (0.007S/m), lungs(0.05S/m), skeletal muscle (0.1S/m) and heart (0.5S/m) [38], and of a specificcondition, hemorrhagic stroke, using a 16-channel system operating at 10MHz [48].In [49], a single channel MIT system measured conductivity from 0.001S/m to 6S/m,encompassing an even greater range of biological tissues including high water contenttissue (this work also validated a theoretical prediction that the induced magnetic fieldis proportional to the conductivity). A full MIT system was later developed to carryout phantom-based biomedical imaging [50], which could detect a conducting tube ofaverage conductivity 0.2S/m at 6cm from the sensor [51]. Imaging results were shownin [52] for conductivity ranging from 0.27S/m to 0.50S/m – equivalent to that of ahuman thigh (depending on the body mass index). The first conductivity image of aleech was presented in [53]; the location and the shape of the leech could be identifiedthrough the reconstructed images.

We have also investigated the feasibility of cryosurgical monitoring using theMIT system shown in Figure 4 [54]. The imaging region is formed by 16 equallyspaced air-cored sensors; each has 6 turns, a side length of 1cm, and a radius of 2cm.The radius of the imaging region is 12cm. Among 16 coils, 8 coils are engaged fortransmitting signals, and the other 8 coils are dedicated for receiving signals; thetotal number of independent measurement is therefore 64. The driving frequency ofthis system is 13MHz. The imaging region was filled with a fluid with an electricalconductivity of 0.9S/m, similar to that of the saline conductivity used in clinicaltreatment. Four different sized insulating bottles (of diameters 2cm, 6.5cm, 9.5 cmand 13cm) are used to represent frozen areas, i.e., the area undergoing cryosurgicaltreatment. Reconstructed images of the frozen areas are shown in Figure 5 and6. The reconstructed images are presented in such a manner that red color showsthe background conductive fluid, and all other colors show the area occupied by theinsulting bottle.

D = 2cm D = 6.5cm D = 9.5cm D = 13cm

Figure 5. Reconstructed images of non-conductive imaging subjects (differentlysized insulated bottles) located in the centre of a saline background with aconductivity of 0.9S/m.


D = 2cm D = 6.5cm D = 9.5cm D = 13cm

Figure 6. Reconstructed images of non-conductive imaging subjects (differentlysized insulated bottles) located off the centre against a saline background with aconductivity of 0.9S/m.

4.2. Industrial process tomography

In the steel industry, an 8-coil MIT system operating at 5kHz was proposed forthe visualisation of metal flows [55]. Laboratory phantom tests were conductedto represent several typical metal flow profiles such as central, annular stream andmultiple streams using metal rods. The MIT system used for this application claimedto have a frame rate of 10 frames/s, which enabled real-time logging of the processdata and online image update. Effort has also been made to image molten flow passingthrough a submerged entry nozzle using this system, with hot trial results consistentwith simulations [43]. In addition, in this paper, the authors also presented a multi-frequency approach to identify a range of samples, which could improve the imagingcapability of MIT for a complex metal flow. Taken together, this is an encouragingstep forward for the commercial development of MIT.

In recent years, MIT has also been used to visualise the conducting phase of amultiphase flow. MIT is considered more advantageous for flow imaging comparedto electrical resistance tomography techniques [56, 57, 58]. However, due to the lowresolution of MIT, the realisation of this technique as a smart imaging device forindustrial process tomography remains a challenging topic, with the experimentalvalidation of two-phase and multi-phase flow imaging still limited. Nevertheless, MITcould be complementary to existing techniques for multi-phase flow imaging as it issensitive to the conductive component of the flow mixtures [59]. A single channelMIT system has been used to measure the water content in multi-phase flow usingexperimental phantom recordings. It was found that the correlation between theposition of the coil and the water/oil interface could be overcome by a full tomographicsystem [60] (a similar conclusion has also been drawn in [61]).

In an attempt to image conductive or ferromagnetic properties in two phase flow,a parallel excitation structure for MIT was shown in [62]. However, this work waslimited in scope, focusing on the simulation of the sensing field only, and as suchexperimental results were not included. It was not until 2008 that a full MIT systemhad demonstrable feasibility for two phase flow imaging. A phantom simulated multi-phase flow in an oil pipeline with a system speed of 90s per frame was carried out in[52]. More recently, experimentally-derived two phase flow images were demonstratedin [36] using a 16 channel MIT system (Figure 4), showing that a conductivity contrastas small as 1.58S/m can be imaged. A further evaluation of the distribution of air


bubbles in a two phase flow using quasi-static experimental data was given in [63]. Astream of bubble gas was injected on the periphery of the flow rig at 2 points oppositeeach other to introduce the perturbation to the electromagnetic field (Figure 7). Thebackground fluid has a conductivity of 5.13S/m, similar to that of the produced water.A snap shot of the bubble testing is reconstructed to show the average bubbles alongthe axial direction (Figure 8). Promising results have also demonstrated how MITcould aid electrical capacitance tomography (ECT) to image a mixture of conductiveand dielectric materials [64]. The further development of MIT-based multi-modalitytomography could therefore be applicable to various industrial processes.

Figure 7. Bubble testing setup, adapted from [63] and reprinted with permissionfrom Elsevier.


Bubble position 1 Bubble position 2

Figure 8. Reconstructed images of bubble flow in a background fluid with aconductivity of 5.13S/m. Adapted from [63] and reprinted with permission fromElsevier.

4.3. Non-destructive evaluation

Non-destructive evaluation (NDE) is vital to public safety and an intrinsicallyinterdisciplinary field, using multiple techniques to inspect the structural integrityof a subject. Many studies have been published to demonstrate the promise of MITin this industry. The earliest concept of using MIT for non-destructive evaluationwas proposed in 1985, to inspect airplane wings for cracks after continued flexing oftheir structure [65]. This work was largely theoretical, although a scanning rig and ananalogue device for one transducer was designed was designed to reconstruct magneticvector potential (but not the conductivity distribution).

In general, MIT offers the considerable benefit of being non-invasive: there is norequirement for direct contact with the material being tested, such as with gels (variousultrasonic methods), specially designed probes (injected current thermography) orelectrodes attached to the composite parts (electrical impedance tomography, EIT).In addition, by using electromagnetic induction to map the spatial resolution, MIThas a non-hazardous data collection process. When compared to X-ray computedtomography, for instance, radiation safety precautions need to be considered, whichcan in certain circumstances be impractical. MIT also has a high temporal resolutionalthough compared to other techniques its image resolution is comparatively low: MITimage reconstruction is an ill-posed problem. More recently, rapid changes in electricalconductivity were captured using MIT alongside Kalman filters and 4D temporallycorrelated imaging [66, 67]. This would potentially enable functional analysis of thetesting structures, of particular interest because this is not currently feasible with anyother existing technique.

Eddy current testing is arguably the most established method in non-destructiveevaluation, although it was not until the 1980s that this technique was fully exploited.In a general sense, both MIT and eddy current testing techniques share manysimilarities – both arose from the same theoretical background (that of Faraday’s lawof induction, and subsequent eddy current theories) and so have similar measurementprinciples, and both are used to image conductive or ferromagnetic materials.Nevertheless, the techniques differ both in their methods of data processing andtheir operation (with eddy current testing usually requiring a certified specialist to


perform). MIT is a tomographic approach and in general more robust, utilising anarray of sensors to create a vector of amplitudes or phase angles from the inducedvoltages, whereas eddy current imaging maps the distribution of the defect within alocalised position using a pair of coils. Decreased electrical potential across these coilsis a measure of their impedance, with impedance related to the location and size ofthe defect.

In [68], MIT was also proposed for industrial pipeline inspection. As MIT coilsare relatively low cost either to make or purchase, coil arrays can be designed for aparticular application. If access is restricted and non-invasive measurements can onlybe taken from one surface, planar MIT is a viable solution. A simulation study ofplanar MIT was reported in [69], where 2D cross-sectional images of conductive barswere obtained using an iterative simultaneous increment reconstruction technique. In[70], a planar MIT system for detecting conductivity inhomogeneity on the surface ofa metallic plate was presented. The experimental realisation of planar MIT has alsobeen extended to 3D subsurface imaging, where aluminium rods can be inspected atdistances of 3-4cm beneath the planar array [71].

In addition to inspecting metallic materials, MIT has also been developedto inspect carbon fiber reinforced polymer (CFRP), a material with widespreadapplication in commercial aircraft, industrial and transportation markets, wherestrength, stiffness, a lower weight, and outstanding fatigue characteristics are crucialrequirements. As the carbon fibres in CFRPs exhibit electrical conductivity, MITcould be a potential NDE technique providing a tomographic approach to traditionaleddy current testing. This was verified in [72] where damages in carbon fiber-reinforced plastics were experimentally investigated. Another 3D experimental studyhas also demonstrated that images of one or more hidden defects inside CFRPscan be reconstructed, although differences in defect size (15 and 25mm diameterholes within CFRP layers) could not be distinguished [73]. Despite the encouragingresults, it is clear that the CFRP samples included in these studies are not sufficientlyrepresentative to cover all possible manufacturing defects or impact damage whichmay occur in a real industrial environment. For example, impact damage couldalter electrical conductivity to a point where conductivity changes are not as highcontrast (and therefore visualisable) as those shown in previous work. Furthermore,some CFRPs could have anisotropic characteristics, requiring the forward problem bemodelled and solved with a high degree of accuracy [74, 75].

5. Discussion

The primary difficulty in applying MIT to biomedical imaging is forward modelling.This is because the sensitivity map (of a conductive inclusion in a free space) isdependent on conductivity contrasts, which might be invalid for biological tissues.Simulations have showed that slight distortions of the receivers could result in 20%deviations to the conductivity perturbation [76]. Even with more accurate sensormodelling, the imaging process can still be demanding, as slight movements of thehuman body (which, for a conscious patient, are inevitable) could corrupt valuableinformation and result in artifacts in the reconstructed image [77]. As such, a full eddycurrent problem not only needs to be solved but updated in an iterative fashion [16];this could significantly increase the computational cost. This cost would increase stillfurther if the forward model is very dense, such as the millions of elements necessaryfor brain imaging.


Furthermore, for a 2D problem, the inverse solver can usually be handled by acentral processing unit (CPU), but for a 3D problem (or any problem with a largenumber of voxels), this could be inefficient for the solving process. High performancecomputing techniques using graphics processing units (GPUs) have been proposed toaddress this, where the parallelisation scheme was implemented on both the forwardand inverse solver [78, 79, 80], significantly reducing computational time.

Although online health monitoring using MIT has yet to be deployed in clinicaltrials, it is nevertheless an imaging technique with great promise. To be realisticallypossible, however, any potential clinical application should allow for MIT datacollection over time, i.e., so that physiological or functional changes can be monitored.

It is common practice to use phantom simulated data to study the feasibility andcapability of MIT both in biomedical imaging and industrial process tomography. Thisis because it is easy to develop phantoms of different sizes, shapes, and conductivitiesat relatively low cost, and to keep the conductivity distribution of the phantoms bothuniform and free from contamination for a lengthy period. In this respect, simulationresults can easily be validated against experimental data. However, the scope ofphantom-based studies is limited in that the experiments are often conducted in staticor quasi-static conditions with limited frame rate (that is, real-time data is usuallyabsent). For example, if accurately imaging a flow of average speed 5m/s, an averageof 20 measurements need to be taken per second (using a commercial capacitancetomography system as a benchmark [81]). This would require a system with a framerate no less than 100 frames per second. At present, however, there is no known MITsystem operating at such frame rate. Although methods to improve the system framerate have been articulated [82], it will likely be some time before the standards of acommercial system can be met – with phantom-based studies unsuited to testing thefeasibility of new developments. In addition, the primary focus of phantom studiesis often imaging the conductivity distribution – the derivation of process parametersfrom the MIT measurements, also of interest to industrial end-users, are not covered.

6. Conclusions

This paper presents an overview of a number of potential applications of MIT andprovides evidential basis for the future exploitation of MIT. The two major challengesfor future development are hardware development, so as to meet the standards ofwidespread commercial applications, and increasing software capability to allow forfully automated real-time image reconstruction and structural analysis of the imagingsubject. In our opinion, successful applications of MIT require an imaging algorithmwith an experimentally verifiable forward model and high-speed hardware capable ofproducing repeatable and stable measurements. In this respect, it is recommendedthat a number of benchmark MIT tests should be developed and adapted by theresearch community for the process of validation of their forward and inverse models.It is hoped that MIT could eventually be commercialised as, for instance, a rapid NDEsystem or a 24/7 health monitoring system, thereby contributing both to the socialeconomy and public good.


Acknowledgments

Figure 6 is reprinted from Progress In Electromagnetics Research, Vol. 131, H. -Y. Wei and M. Soleimani, Two-phase low conductivity flow imaging using magneticinduction tomography, Pages No.99–115., Copyright (2012), with permission from theThe Electromagnetics Academy.Figure 9 and 10 are reprinted from The International Journal of Multiphase Flow,Vol. 72, L. Ma, A. Hunt and M. Soleimani, Experimental Evaluation of ConductiveFlow Imaging Using Magnetic Induction Tomography, Pages No.198-209., Copyright(2015), with permission from Elsevier.

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University of Bath · the forward problem, the ﬁnite element method (FEM) is employed to evaluate the ﬁeld distribution. This is then used to derive a sensitivity matrix that